Tuesday, November 21, 2023

2023-11-28 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 대수기하학:

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2023-11-22 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 위상수학 세미나:

by 김민규(고등과학원)

Finite path integral is a finite version of Feynman’s path integral, which is a mathematical methodology to construct TQFT’s (topological quantum field theories) from finite gauge theory. It was introudced by Dijkgraaf and Witten in 1990. We study finite path integral model by replacing finite gauge theory with homological algebra based on bicommutative Hopf algebras. It turns out that Mayer-Vietoris functors such as homology theories extend to TQFT which preserves compositions up to a scalar. This talk concerns the second cohomology class of cobordism (more generally, cospan) categories induced by such scalars. In particular, we will explain that the obstruction class is described purely by homological algebra, not via finite path integral.

2023-11-27 / 10:00 ~ 11:00

학과 세미나/콜로퀴엄 - 박사논문심사: 무한 너비 신경망의 두터운 꼬리 분포와 노드간 의존성

by 이호일(KAIST)

2023-11-21 / 16:00 ~ 17:00

학과 세미나/콜로퀴엄 - 박사논문심사: 불균질 위치 점프 과정과 확산 법칙

by 임현진(KAIST)

2023-11-22 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - BK21세미나:

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Zeta functions and zeta values play a central role in Modern Number Theory and are connected to practical applications in codes and cryptography. The significance of these objects is demonstrated by the fact that two of the seven Clay Mathematics Million Dollar Millennium Problems are related to these objects, namely the Riemann hypothesis and the Birch and Swinnerton-Dyer conjecture. We first recall results and well-known conjectures concerning these objects over number fields. If time permits, we will present recent developments in the setting of function fields. This is a joint work with Im Bo-Hae and Kim Hojin among others.

2023-11-28 / 16:30 ~ 17:30

IBS-KAIST 세미나 - 이산수학: Towards a high-dimensional Dirac’s theorem

by 이현우(KAIST & IBS 극단조합및확률그룹)

Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. We consider another natural generalization of the perfect matchings, Steiner triple systems. As a Steiner triple system can be viewed as a partition of pairs of vertices, it is a natural high-dimensional analogue of a perfect matching in graphs. We prove that for sufficiently large integer $n$ with $n \equiv 1 \text{ or } 3 \pmod{6},$ any $n$-vertex $3$-uniform hypergraph $H$ with minimum codegree at least $\left(\frac{3 + \sqrt{57}}{12} + o(1) \right)n = (0.879... + o(1))n$ contains a Steiner triple system. In fact, we prove a stronger statement by considering transversal Steiner triple systems in a collection of hypergraphs. We conjecture that the number $\frac{3 + \sqrt{57}}{12}$ can be replaced with $\frac{3}{4}$ which would provide an asymptotically tight high-dimensional generalization of Dirac's theorem.

2023-11-22 / 16:00 ~ 17:00

IBS-KAIST 세미나 - 수리생물학:

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I will report on some recent results on modelling the heart, the external circulation, and their application to problems of clinical relevance. I will show that a proper integration between PDE-based and machine-learning algorithms can improve the computational efficiency and enhance the generality of our iHEART simulator.

2023-11-23 / 14:30 ~ 16:00

학과 세미나/콜로퀴엄 - 기타:

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(information) "Introduction to Oriented Matroids" Series Thursdays 14:30-15:45

2023-11-23 / 16:15 ~ 17:15

학과 세미나/콜로퀴엄 - 콜로퀴엄:

by 박지원()

In the analysis of singularities, uniqueness of limits often arises as an important question: that is, whether the geometry depends on the scales one takes to approach the singularity. In his seminal work, Simon demonstrated that Lojasiewicz inequalities, originally known in real algebraic geometry in finite dimensions, can be applied to show uniqueness of limits in geometric analysis in infinite dimensional settings. We will discuss some instances of this very successful technique and its applications.

2023-11-21 / 16:00 ~ 17:00

SAARC 세미나 - SAARC 세미나: Colloquium: An Optimal Transport Approach to Understanding the Interface Between Water and Ice

by 김영헌(UBC Math)

The Stefan problem is a free boundary problem describing the interface between water and ice. It has PDE and probabilistic aspects. We discuss an approach to this problem, based on optimal transport theory. This approach is related to the Skorokhod problem, a classical problem in probability regarding the Brownian motion.

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